PSI - Issue 18

L. Collini et al. / Procedia Structural Integrity 18 (2019) 671–687 L. Collini / Structural Integrity Procedia 00 (2019) 000–000

679

9

4.3. Ferrite damage The damage of the ferrite phase is here modeled with the Abaqus TM ductile damage, which is a phenomenological model for predicting the onset of damage due to nucleation, growth, and coalescence of voids. The model assumes that the equivalent plastic strain at the onset of damage is a function of the stress triaxiality and strain rate, where    p q is the local stress triaxiality with p the hydrostatic pressure and q the deviatoric stress at the micro-scale. The damage initiation is satisfied when:

(6)

where ω D is a state variable that increases monotonically as Δω D increases with the plastic deformation for each increment of plastic strain   D pl . In this study, for the ferritic phase the fracture strain vs. stress triaxiality dependence is assumed to be an exponential law of the Johnson-Cook type:

 3 

(7)

1   2 e

pl  

 D

.

The parameters in Eq. (7) are reported in Tab. 5, and the represented in graphical form is depicted in Fig. 5. This assumption is supported by behavior of α-ferrite and ferritic steels observed in experimental tests under variable triaxiality conditions, Hancock et al. (1976), Johnson et al. (1985), Mirza et al. (1996), Maresca (1997), Hopperstad et al. (2003), Bao et al. (2004, 2009), Ohata et al. (2008), Springer (2012), Cheng et al. (2017), Hradil et al. (2017). For negative stress triaxiality values, if no data are available no dependency is assumed and failure strain is kept constant, Manjoine (1982).

Fig. 5. Equivalent strain at the onset of damage of ferrite.

Once the initiation criterion of Eq. (6) is satisfied, the material stiffness is progressively degraded by the FE analysis according to a specified damage evolution law for the criterion, having effect on the material response and eventually leading to the material failure. Here, in conjunction with the ductile damage model Abaqus TM assumes that the degradation of the stiffness follows a scalar damage variable, and at any given time during the analysis the stress tensor in the material is given by the scalar damage equation: s  1  D   s (8)